/*
 *                               POK header
 *
 * The following file is a part of the POK project. Any modification should
 * be made according to the POK licence. You CANNOT use this file or a part
 * of a file for your own project.
 *
 * For more information on the POK licence, please see our LICENCE FILE
 *
 * Please follow the coding guidelines described in doc/CODING_GUIDELINES
 *
 *                                      Copyright (c) 2007-2021 POK team
 */

/* @(#)e_hypot.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

/* __ieee754_hypot(x,y)
 *
 * Method :
 *	If (assume round-to-nearest) z=x*x+y*y
 *	has error less than sqrt(2)/2 ulp, than
 *	sqrt(z) has error less than 1 ulp (exercise).
 *
 *	So, compute sqrt(x*x+y*y) with some care as
 *	follows to get the error below 1 ulp:
 *
 *	Assume x>y>0;
 *	(if possible, set rounding to round-to-nearest)
 *	1. if x > 2y  use
 *		x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
 *	where x1 = x with lower 32 bits cleared, x2 = x-x1; else
 *	2. if x <= 2y use
 *		t1*yy1+((x-y)*(x-y)+(t1*y2+t2*y))
 *	where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
 *	yy1= y with lower 32 bits chopped, y2 = y-yy1.
 *
 *	NOTE: scaling may be necessary if some argument is too
 *	      large or too tiny
 *
 * Special cases:
 *	hypot(x,y) is INF if x or y is +INF or -INF; else
 *	hypot(x,y) is NAN if x or y is NAN.
 *
 * Accuracy:
 * 	hypot(x,y) returns sqrt(x^2+y^2) with error less
 * 	than 1 ulps (units in the last place)
 */

#ifdef POK_NEEDS_LIBMATH

#include "math_private.h"

double __ieee754_hypot(double x, double y) {
  double a = x, b = y, t1, t2, yy1, y2, w;
  int32_t j, k, ha, hb;

  GET_HIGH_WORD(ha, x);
  ha &= 0x7fffffff;
  GET_HIGH_WORD(hb, y);
  hb &= 0x7fffffff;
  if (hb > ha) {
    a = y;
    b = x;
    j = ha;
    ha = hb;
    hb = j;
  } else {
    a = x;
    b = y;
  }
  SET_HIGH_WORD(a, ha); /* a <- |a| */
  SET_HIGH_WORD(b, hb); /* b <- |b| */
  if ((ha - hb) > 0x3c00000) {
    return a + b;
  } /* x/y > 2**60 */
  k = 0;
  if (ha > 0x5f300000) {    /* a>2**500 */
    if (ha >= 0x7ff00000) { /* Inf or NaN */
      uint32_t low;
      w = a + b; /* for sNaN */
      GET_LOW_WORD(low, a);
      if (((ha & 0xfffff) | low) == 0)
        w = a;
      GET_LOW_WORD(low, b);
      if (((hb ^ 0x7ff00000) | low) == 0)
        w = b;
      return w;
    }
    /* scale a and b by 2**-600 */
    ha -= 0x25800000;
    hb -= 0x25800000;
    k += 600;
    SET_HIGH_WORD(a, ha);
    SET_HIGH_WORD(b, hb);
  }
  if (hb < 0x20b00000) {    /* b < 2**-500 */
    if (hb <= 0x000fffff) { /* subnormal b or 0 */
      uint32_t low;
      GET_LOW_WORD(low, b);
      if ((hb | low) == 0)
        return a;
      t1 = 0;
      SET_HIGH_WORD(t1, 0x7fd00000); /* t1=2^1022 */
      b *= t1;
      a *= t1;
      k -= 1022;
    } else {            /* scale a and b by 2^600 */
      ha += 0x25800000; /* a *= 2^600 */
      hb += 0x25800000; /* b *= 2^600 */
      k -= 600;
      SET_HIGH_WORD(a, ha);
      SET_HIGH_WORD(b, hb);
    }
  }
  /* medium size a and b */
  w = a - b;
  if (w > b) {
    t1 = 0;
    SET_HIGH_WORD(t1, ha);
    t2 = a - t1;
    w = __ieee754_sqrt(t1 * t1 - (b * (-b) - t2 * (a + t1)));
  } else {
    a = a + a;
    yy1 = 0;
    SET_HIGH_WORD(yy1, hb);
    y2 = b - yy1;
    t1 = 0;
    SET_HIGH_WORD(t1, ha + 0x00100000);
    t2 = a - t1;
    w = __ieee754_sqrt(t1 * yy1 - (w * (-w) - (t1 * y2 + t2 * b)));
  }
  if (k != 0) {
    uint32_t high;
    t1 = 1.0;
    GET_HIGH_WORD(high, t1);
    SET_HIGH_WORD(t1, high + (k << 20));
    return t1 * w;
  } else
    return w;
}

#endif
